Material is always black and on Cycles
The mesh has custom split normals in the problematic area. In order to see the split normals, switch to edit mode and enable Display Split Normals in the Viewport Overlays.

Viewport Overlays



Problematic Normals



If you have created the split normals intentionally you can edit them until they match the desired result (consult the manual for ways to edit normals). In case the custom split normals were created by accident and you don't want them, they can be deleted in Object Data Properties > Geometry Data > Clear Custom Split Normals Data.

Clear custom split normals



Fixed Normals



When custom split normals are stored, Auto Smooth is automatically enabled. It can be disabled in Object Data Properties > Normals > Auto Smooth, in case you don't need it.

Disable Auto Smooth